for the Electric Fields of Distributed Charge An evenly charged wire of length L has a total charge of Q distributed on it and is located on the x-axis a distance a away from the origin as drawn. Set up the integrals that could be solved to determine the (0, yo) vector electric field components, E = (Ex,Ey), at any point on the %3D y-axis, (0, yo). You should NOT evaluate the integrals.
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- E. When E and A were parallel, we called the quantity EA the electric flux through the surface. For the parallel case, we found that EA is proportional to the number of field lines through the surface. By what trigonometric function of 0 must you multiply EA so that the product is proportional to the number of field lines through the area for any orientation of the surface? Rewrite the quantity described above as a product of just the vectors E and A.Question 1 Four stationary electric charges produce an electric field in space. The electric field depends on the magnitude of the test charge used to trace the field O has different magnitudes but same direction everywhere in space is constant everywhere in space has different magnitude and different directions everywhere in space CANADa) Find the surface charge density σ2 of the cylindrical shell of radius R2. (Note the unit in the input box and the sign of charges.) Surface charge density σ2Give your answer up to at least three significance digits. b) Find an expression of electric field at rmm from the center where R1<r<R2. Assume the cylinder has a length L and L is very long so that electric field is uniform. Consider that the insulating material between the cylinders is air. (Hint : use Gauss's law and cylindrical Gaussian surface with radius r.) Magnitude of the electric field at r=0.76mm Give your answer up to at least three significance digits. c) Calculate absolute value of the potential difference between the wire and the cylinder. Absolute value of the potential difference Give your answer up to at least three significance digits. d) Calculate the capacitance C for this cylindrical system. Assume that the length of the cylinder is L=17cm. Capacitance C for this cylindrical system Give your…
- Two oppositely charged but otherwise identical conducting plates of area 2.50 square centimeters are separated by a dielectric 1.80 millimeters thick, with a dielectric constant of K = 3.60. The I can't found part c resultant electric field in the dielectric is 1.20 x 10° volts per meter. Part A Compute the magnitude of the charge per unit area o on the conducting plate. Express your answer in coulombs per square meter to three significant figures. • View Available Hint(s) o = 3.82x10-5 C/m² Submit Previous Answers Correct Part B Compute the magnitude of the charge per unit area o1 on the surfaces of the dielectric. Express your answer using three significant figures. • View Available Hint(s) ơ1 = 2.76x10-5 C/m² Submit Previous Answers Correct Note that the charges on the dielectric will be polarized to counteract the charges (and electric field) created by the capacitor. For example, near the positive surface of the capacitor the dielectric will have a negative charge. However, this…Charge is distributed throughout a spherical shell of inner radius ₁ and outer radius r2 with a volume density given by p= Por1/r, where po is a constant. Following the next few steps outlined, determine the electric field due to this charge as a function of r, the distance from the center of the shell. Hint a. Let's start from outside-in. For a spherical Gaussian surface of radius r>r2, how much charge is enclosed inside this Gaussian surface? Hint for finding total charge Qencl (Answer in terms of given quantities, po, r1, 72, and physical constants ke and/or Eo. Use underscore ("_") for subscripts, and spell out Greek letters.) b. What is the electric field as a function of r for distances greater than r₂? Finish the application of Gauss's Law to find the electric field as a function of distance. E(r> r₂) c. Now let's work on the "mantle" layer, r₁Charge is distributed throughout a spherical shell of inner radius r₁ and outer radius r2 with a volume density given by p= Pori/r, where po is a constant. Following the next few steps outlined, determine the electric field due to this charge as a function of r, the distance from the center of the shell. Hint a. Let's start from outside-in. For a spherical Gaussian surface of radius r > r2, how much charge is enclosed inside this Gaussian surface? Hint for finding total charge Because the charge density is a function of r, rather than being able to multiply the charge density by the volume, row you need to integrate over the volume. The amount of charge in a spherical shell of radius r and thickness dr is p(r). 4tr²dr; integrate this from r = r₁ to r = r₂ to obtain the total amount of charge. Qencl= (Answer in terms of given quantities, po, 71, 72, and physical constants ke and/or Eo. Use underscore ("") for subscripts, and spell out Greek letters.) b. What is the electric field as a…Charge is distributed throughout a spherical shell of inner radius and outer radius 72 with a volume density given by p= Pori/r, where Po is a constant. Following the next few steps outlined, determine the electric field due to this charge as a function of 7, the distance from the center of the shell. Hint a. Let's start from outside-in. For a spherical Gaussian surface of radius > ₂ how much charge is enclosed inside this Gaussian surface? Hint for finding total charge Qencl (Answer in terms of given quantities, Po. 71, 72, and physical constantske and/or £g. Use underscore ("_") for subscripts, and spell out Greek letters.) b. What is the electric field as a function of for distances greater than 72? Finish the application of Gauss's Law to find the electric field as a function of distance. E(T > T₂) c. Now let's work on the "mantle" layer, ₁ <<₂. For a spherical surface of radius & between T₁ and ₂. how much charge is enclosed inside this Gaussian surface? Hint for finding charge…Charge is distributed throughout a spherical volume of radius R with a density p = ar², where a is a constant (of unit C/m³, in case it matters). Determine the electric field due to the charge at points both inside and outside the sphere, following the next few steps outlined. Hint a. Determine the total amount of charge in the sphere. Hint for finding total charge Qencl = (Answer in terms of given quantities, a, R, and physical constants ke and/or Eg. Use underscore ("_") for subscripts, and spell out Greek letters.) b. What is the electric field outside the sphere? E(r> R) = c. What is the electric field inside the sphere? Hint for E within sphere #3 Question Help: Message instructor E(r < R) = Submit Question E с $ 4 R G Search or type URL % 5 T ^ MacBook Pro 6 Y & 7 U * 8 9 0 0Part A through part D, please Charge is distibuted uniformly over each of two spherical volumes with radius R. One sphere of charge is centered at the origin and the other at x=2R (Figure 1). Let left-hand sphere have positive charge Q and let the right-hand sphere have negative charge -Q . Part A Find the magnitude of the net electric field due to these two distributions of charge at the point x=0 on the x-axis. Express your answer in terms of the variables Q , R , and appropriate constants. Part B Find the magnitude of the net electric field at the point x=R/2 on the x-axis. Express your answer in terms of the variables Q , R , and appropriate constants. Part C Find the magnitude of the net electric field at the point x=R on the x-axis. Express your answer in terms of the variables Q, R , and appropriate constants. Part D Find the magnitude of the net electric field at the point x=3Ron the x-axis. Express your answer in terms of the variables Q, R, and appropriate constants.Consider a thin plastic rod bent into an arc of radius Rand angle a (see figure below). The rod carries a uniformly distributed negative charge Q -Q A IR What are the components and E, of the electric field at the origin? Follow the standard four steps. (a) Use a diagram to explain how you will cut up the charged rod, and draw the AE contributed by a representative piece. (b) Express algebraically the contribution each piece makes to the and y components of the electric field. Be sure to show your integration variable and its origin on your drawing. (Use the following as necessary: Q, R, cx, 0, A0, and EQ-) ΔΕ, = - TE aR² AB=(2 Lower limit= 0 ✓ e aR² Upper limit= a X cos(0)40 x (c) Write the summation as an integral, and simplify the integral as much as possible. State explicitly the range of your integration variable. sin (0)40 x Evaluate the integral. (Use the following as necessary: Q, R, a, and E.) EditConst A charge of 87.6 pC is uniformly distributed on the surface of a thin sheet of insulating material that 2 has a total area of 95.2 cm. A Gaussian surface encloses a portion of the sheet of charge. Part A If the flux through the Gaussian surface is 7.80 N. m? /C, what area of the sheet is enclosed by the Gaussian surface? Express your answer with the appropriate units. Value Units A =Electric Fields 3. A plastic rod is bent into the quarter circle of radius R as shown below. A total positive charge of Q is evenly distributed along the rod. a. In terms of the given quantities, what is the linear charge density A? b. Set up the two integrals you would evaluate to find the components of the electric field. The integrals should be written in terms of the given quantities {Q and R} Ex Ey с. Evaluate your integrals to write down the electric field vector at the origin. y E = -f 10 + +SEE MORE QUESTIONS
